JP4848320B2 - Parameter identification apparatus and program thereof - Google Patents

Description

  The present invention performs a simulation using a nonlinear physical model, compares the output with the output to be optimized, and repeatedly corrects the parameters of the physical model based on the comparison result, thereby asymptotically bringing each parameter to a true value. It relates to the identification of parameters to be performed.

  Conventionally, simulation using a model has been performed, and for this purpose, a model in accordance with the actual situation is required. For this reason, it is necessary to determine the specifications of the model, and the specifications of the model are identified from experimental data. In this case, a process for determining whether the identification has been performed with high accuracy is required.

  Here, Patent Document 1 describes that an adaptive controller is mounted on the vehicle, and an adaptive parameter of the internal combustion engine is calculated by the adaptive controller to control fuel injection of the internal combustion engine. And in this patent document 1, when adjusting various adaptive parameters, by setting the identification error signal which determines the change speed of an adaptive parameter to a predetermined range, even if an identification error signal fluctuates, adaptive parameter It has been shown that a good controllability can be obtained by stabilizing the rate of change of. It is also described that the range of the identification error signal is set according to the operating state.

JP-A-8-291746

  As described above, in Patent Document 1, the identification error signal for determining the change speed of the adaptive parameter is set within a predetermined range, thereby stabilizing the change speed of the adaptive parameter and improving the controllability. That is, by limiting the change speed of the adaptation parameter, the adaptation parameter is easily converged to an appropriate value. However, in this method, since the change speed is slow, there is a demand for a relatively long time until convergence and to shorten the time until convergence.

  The present invention performs a simulation using a nonlinear physical model, compares the output with the output to be optimized, and repeatedly corrects the parameters of the physical model based on the comparison result, thereby asymptotically bringing each parameter to a true value. An apparatus for identifying a parameter, wherein the upper and lower limit values are sequentially changed by setting upper and lower limit values for a parameter correction amount based on an error change amount obtained in the comparison. To do.

  Further, it is preferable that the change amount of the error obtained in the comparison is a difference between the error of the previous output and the error of the current output.

  The error is preferably a sum of squares of an error between an output to be optimized and a model output in a predetermined period, and the correction amount is preferably determined based on a gradient with respect to a change in a parameter of the sum of squares.

  Furthermore, the present invention relates to a program that causes a computer to execute the above processing by being executed in the above apparatus.

  As described above, according to the present invention, the parameter correction amount is restricted based on the obtained error, so that the parameter identification can be converged relatively quickly.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings.

  FIG. 2 shows a schematic configuration of a hydraulic system to be identified in the present embodiment. An automatic transmission is connected to the engine, and the rotation of the engine output shaft is changed by this automatic transmission and transmitted to the tire. The automatic transmission receives a hydraulic pressure and performs a shift operation. For example, when the shift timing comes according to the running state of the vehicle, an ECU (electronic control unit) detects this, supplies a current according to the shift command to the hydraulic control circuit, and in the hydraulic control circuit automatic transmission The shift operation is performed by controlling the hydraulic pressure to the clutch pack.

  Here, the hydraulic system of the automatic transmission has a hydraulic pump driven by an engine, and oil from the hydraulic pump is supplied to the hydraulic line. A hydraulic pressure adjusting valve is provided near the hydraulic pump in the hydraulic line, and thereby the line pressure (original pressure) in the hydraulic line is controlled to a predetermined value. A linear solenoid valve is provided in the hydraulic line, and the supply of the line pressure of the hydraulic line to the clutch pack is controlled. Note that an orifice is provided in the flow path from the linear solenoid valve to the clutch pack to limit the supply of hydraulic pressure to the clutch pack. The clutch pack controls the engagement / release of the input side disk and the output side disk by moving the piston against the spring pressure by hydraulic pressure. For example, when shifting from the first speed to the second speed, the first-speed output disk originally engaged with the input-side disk is released, and the second-speed output disk is engaged.

  Considering such a hydraulic system to be controlled, the input is a hydraulic pressure command value, and the output is the hydraulic pressure supplied to the clutch pack.

  FIG. 3 shows an overview of parameter identification in the present embodiment. It shows that the parameters (i) to (iv) in the detailed hydraulic model are identified based on the error between the hydraulic system output of the actual machine and the model output. In this example, the parameters are (i) the time constant of the hydraulic system, (ii) the clogging position of the clutch pack, (iii) the clutch operating load, and (iv) the hydraulic dead zone. The oil pressure command value is supplied to the oil pressure detailed model. This hydraulic detail model is composed of a design condition model and a characteristic variation model. Then, by inputting the hydraulic pressure command value, the hydraulic pressure supplied to the clutch pack is output from the detailed hydraulic model. The hydraulic pressure command value is also supplied to the actual hydraulic system to measure the hydraulic pressure that is actually output. Then, the error between the two is calculated and supplied to the identification (optimization) method. In the identification method, the characteristic parameter of the characteristic variation model in the hydraulic detail model is changed according to the error, and new parameters for parameters (i) to (iv) are set in the characteristic variation model. As a result, the next hydraulic detail model is set and the operation of obtaining this output is repeated.

  FIG. 4A shows a block diagram of the hydraulic system. First, a shift command is supplied to the ECU. The ECU supplies a signal for operating the linear solenoid valve in response to the shift command. Actually, both a release signal for the linear solenoid valve of the release hydraulic line and an engagement signal for the linear solenoid valve of the engagement hydraulic line are both used. As a result, the oil accompanying the operation of the linear solenoid valve is supplied to the orifice flow path to the clutch pack, and the clutch pressure is determined. Note that the flow rate of the orifice channel is q, the clutch piston stroke in the clutch pack is xc, the clutch area Ac, and the clutch pressure Pc.

  FIG. 4B shows the specifications of the hydraulic system to be identified. When a shift command is input, the ECU generates a delay with respect to this command. In this example, the delay is expressed by 1 / (T · s + 1), where T is a time constant, which is the parameter (i). Further, the linear solenoid valve has a dead zone until the operation starts, and this is the parameter (iv).

Orifice, the flow rate qc is determined by _{qc = C 0 · Ac√ {2} (Pl-Pc) / ρ}. Here, Pl is the upstream pressure of the orifice, Pc is the clutch pack side pressure, ρ is the density of the oil, and C ₀ is a constant relating to the viscosity (opening ratio, Reynolds number) of the oil.

  In the clutch pack, the clutch piston stroke xc and the clutch pressure PC are expressed as xc = ∫qcdt / Ac, Pc = Kc · xc / Ac. Kc is a constant. Furthermore, the operation of the clutch pack is greatly affected by the clogging of the pack. Therefore, the pack clogging position is set to xc_max, and the clutch pressure at that position is set to Pc_max. Therefore, at the pack clogging position, xc = xc_max, Pc = Kc · xc_max / Ac = PC_max.

  Next, parameter identification in the present embodiment will be described with reference to the flowcharts of FIGS. 1A and 1B. In the description, the output of the hydraulic detail model in which the values of the parameters (i) to (iv) are appropriately changed is used instead of the output data of the actual machine.

  First, in step 1, initial (nominal) values [a (1) b (1) c (1) d (1)] of model parameters to be identified (optimized) are determined. This nominal value is preferably set to a value that is normally conceivable. In this example, the hydraulic system specifications to be identified are indicated by broken-line circles in FIG. 4B.

  In steps 2 and 3, the model is simulated, and an error between the model output and the actual machine output is obtained as shown in FIG. In the present embodiment, the sum of squares of this error is used as an evaluation value, and this is calculated according to formula (1) or formula (2). Expression (1) is a case of a continuous system of analog data, and Expression (2) is a case of a discrete system using sampling data. In the case of a continuous system, it is a value obtained by integrating the square of the error of the output hydraulic pressure Pc from time t = 0 to tf, and in the case of a discrete system, it is 1 / N of the square sum of the errors of N samples. .

  Subsequently, in step 4, if the error (evaluation value: sum of squares of error) in equation (1) or equation (2) is within a threshold, the target output is obtained and the identification step is terminated.

If NO in step 4, that is, if the error (evaluation value) is larger than the threshold value, the process proceeds to step 5 to set a new parameter obtained by appropriately shifting the initial value of the model parameter (formula (3)).
[a (1) b (1) c (1) ...] = [a (1) + δ ₁ b (1) + δ ₂ c (1) + δ ₃ ...] (3)

  In step 6, model simulation is performed in the same manner as in step 2 using the parameters of equation (3). In step 7, an error (evaluation value) is calculated again using equation (1) or equation (2). It is determined whether (evaluation value) is within a threshold value. If the determination in step 8 is within the threshold value, the identification step ends. On the other hand, if it is determined in step 8 that the error (evaluation value) is larger than the threshold value, the process proceeds to step 9.

  In step 9, a gradient vector is calculated from the factor effect of each parameter. For this purpose, first, with respect to the four parameters (i) to (iv) shown in FIGS. 3 and 4B, combinations of two levels (two values for one parameter) as shown in Table 1, Sixteen patterns are prepared, and error sums of squares J1 to J16 are calculated for each combination.

  As shown in Table 2, the factor effect (average value for each level) is calculated for each parameter level (2 levels) from the obtained error.

That is, J _a (1) is the average value (evaluation value) of the square sum of errors when the parameter (hydraulic system time constant) is a (1) (level 1), and J _a (2) is the parameter ( This is an average value of the sum of squares of errors when the hydraulic system time constant) is a (2) (level 2). Similarly, Jb (1), Jb (2), Jc (1), Jc (2), Jd (1), Jd (2) are average values of the evaluation values at the levels 1 and 2 for each parameter. . Therefore, Table 2 shows the effect of each parameter on the level 1 and 2 changes.

  From the factor effects in Table 2, the gradient vector [Sa (1) Sb (1) Sc (1) Sd (1)] of the entire parameter defined by Expression (4) is obtained. That is, each element of the gradient vector is an output gradient with respect to levels 1 and 2 of one parameter.

  In step 10, the parameter correction amount is calculated based on the gradient vector S (i). Here, i indicates the number of calculations, and the above levels 1 and 2 represent those used for the first and second calculations, i = 3 in the third calculation, and level 1 I = 2 and level 2 is i = 3.

  The next model parameter is calculated by equation (5) using the scalar value k.

  In this way, the next parameter is determined by adding the correction amount corresponding to the evaluation value for each parameter. When the next parameter is determined, the process returns to step 6 and the same steps are repeated until the error becomes equal to or less than the threshold value.

In this way, it is possible to identify a parameter (= hydraulic specification) whose error is equal to or less than a predetermined value.
"Restrictions on correction amount"

  Here, in this embodiment, step 20 shown in FIG. 1B is provided between step 9 and step 10 in FIG. 1A. That is, in step 20, the size of each element of the gradient vector S (i) in the equation (4) is limited according to the square sum of errors.

  That is, when the gradient vector [Sa (i) Sb (i) Sc (i) Sd (i)] is calculated in step 9, the obtained gradient Sa (i) of one parameter a is the upper limit. It is compared with the value Samax (step 21). If the determination in step 21 is Yes, Sa (i) = Samax is set (step 22). In this example, Samax = √ [(1/2) · (Ja (i) / k)]. If the determination in step 21 is No, the process in step 22 is not performed.

  Next, the gradient Sa (i) is compared with the lower limit value -Samax (step 23). If the determination in step 23 is Yes, Sa (i) = − Samax is set (step 24). If the determination in step 23 is No, the process of step 24 is not performed.

  Similarly, when the same processing is performed for all parameters, the upper and lower limits are exceeded for the gradients Sa (i), Sb (i), Sc (i), and Sd (i) for all parameters. This can be set to upper and lower set values.

  In this manner, the upper and lower limit values are restricted by the step 20 for each element of the gradient vector [Sa (i) Sb (i) Sc (i) Sd (i)].

  Then, a gradient vector in which the upper and lower limit values are applied to each element is supplied to step 10, and each parameter is corrected based on the gradient vector.

  Next, the limitation on the correction amount will be specifically described. First, the basic concept is shown in FIG. This figure shows that the parameter when the number of corrections is i is a (i), and the square sum of the error between the model and the actual output is J (i). At this time, the change amount ΔJ (i) = J (i + 1) −J (i) of the square sum of errors J (i + 1) at the time of correction i + 1 falls within a certain range, for example, a range of 1/2 * J (i). Thus, if the size of the gradient vector in equation (4) is limited, the square sum of errors J (i) can only be within a certain amount of change (in the range of 1/2 * J (i)). Since it does not change, the convergence of the identification parameter is considered to be stable.

  Next, the above idea is specifically expressed by an expression. In the relational expression of Expression (5), the parameter a will be described as an object (Expression (6)).

  a (i + 1) = a (i) + k · Sa (i) (6)

  Here, i is the number of corrections.

  The change amount ΔJ (i) of the sum of squares of the error in FIG. 5 can be calculated as in Expression (7).

  Here, in order to simplify the derivation of the threshold value, it is assumed that the corrected i-th gradient Sa (i) and the corrected i + 1-th gradient Sa (i + 1) have the same value. At this time, Equation (7) is the maximum gradient value Samax (i). That is, using the threshold value and the maximum value | ΔJ (i) | max of the error sum of squares of error, it can be written as equation (7) ′, and the threshold value is derived from the equation as equation (8). .

  Assuming that | ΔJ (i) | max = | (1/2) J (i) | as the maximum value | ΔJ (i) | max of the change amount of the square sum of errors, for example, Equation (8) 8) '.

  Note that the denominator of | (1/2) J (i) | does not have to be 2, and a value of 2 to n (n: positive value) may be set as appropriate. In this way, the threshold value for the correction amount can be set, and the correction amount can be limited according to the calculation result (sum of squares of errors) each time.

  6 and 7 show the results of identification by applying this embodiment. It can be seen that the parameter is stably converged to the true value after about 15 corrections.

  8 and 9 show the results of identification without any limitation under the same conditions (initial values of parameters and correction gain) as in FIGS. 6 and 7. FIG. 8 shows the time-series waveform of the identification results, FIG. These are figures which show the change of each parameter by correction.

  Further, FIGS. 10 and 11 identify the gradient vector within the predetermined range (threshold value) in which the parameter can be stably converged under the same condition (initial value of parameter, correction gain) as in FIGS. FIG. 10 is a time-series waveform of identification results, and FIG. 11 is a diagram showing changes in parameters due to correction. In this way, the parameter is stably converged to the true value. However, it can be seen that the number of times of convergence until convergence is as high as about 50, and the convergence speed is slow.

It is a flowchart which shows the process of parameter identification. It is a flowchart which shows the process which sets the upper and lower limit value of the parameter correction amount. It is a figure which shows the outline | summary of a hydraulic control system. It is a figure which shows the outline | summary of the identification method of a parameter. It is a block diagram of a hydraulic system. It is a figure which shows the item of the hydraulic system to identify. It is a figure which shows how to apply the restriction | limiting with respect to the magnitude | size of a gradient vector. Identification result 1: It is a figure which shows a time series waveform. Identification result 2: It is a figure which shows the square sum of a parameter value and an error. Identification result 1: It is a figure which shows a time series waveform. Identification result 2: It is a figure which shows the square sum of a parameter value and an error. Identification result 1: It is a figure which shows a time series waveform. Identification result 2: It is a figure which shows the square sum of a parameter value and an error.

Claims (4)

A parameter that makes each parameter asymptotic to a true value by performing a simulation using a nonlinear physical model, comparing the output with the output of the optimization target, and repeatedly correcting the parameters of the physical model based on the comparison result The identification device of
An apparatus for identifying a parameter, wherein the upper and lower limit values are sequentially changed by setting upper and lower limit values for a parameter correction amount based on an error change amount obtained in the comparison. The parameter identification device according to claim 1,
An apparatus for identifying a parameter, characterized in that the amount of error change obtained in the comparison is a difference between a previous output error and a current output error. In the parameter identification device according to claim 1 or 2,
The error is a square sum of an error between an output to be optimized and a model output in a predetermined period, and the correction amount is determined based on a gradient with respect to a change in a parameter of the sum of squares. . A parameter that makes each parameter asymptotic to a true value by performing a simulation using a nonlinear physical model, comparing the output with the output of the optimization target, and repeatedly correcting the parameters of the physical model based on the comparison result A parameter identification program for causing a computer to execute the identification process of
A parameter identification program that causes a computer to execute a step of sequentially changing the upper and lower limit values by setting upper and lower limit values for a parameter correction amount based on an error obtained in the comparison.

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